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Electric Fields, Charge Distributions, and the GRE

Reviewing for the GRE physics subject test, I've frequently come across questions like: Given a distribution of discrete charges, (as shown in the diagram), determine the electric field at a given point r, (also shown in the diagram). Formula for the Electric Field from a Distribution of Charges The distribution of charges I've seen in sample questions have, so far, involved only finite numbers of point charges, so the electric field equation can be written as a sum: where is the distance from a charge contributing to the sum to the location where the electric field is being measured, q is the value of the particular charge, and u is the unit vector pointing from the contributing charge to the field measurement point. This can be separated into x and y components: where theta is the angle between the particular charge and the point where the field is being measured with respect to the x axis. Using these formulas, it's just a matter of summing up the contribution of each ...

Fourth of July Trailhead on the Fourteenth of October

Snow is already coming down all over Colorado! In fact, they opened a few of the ski runs today! I traveled up to Diamond Lake via the Fourth of July trailhead yesterday where there's just a little bit of snow in the shady spots. The hike is beautiful, it crosses two very nice waterfalls and Boulder Creek on the way up. I ran into three other groups making the trek on a Tuesday afternoon. For more information on the trail and the Forest Service regulations for the area check: Diamond Lake [pdf] Pictures Back down the valley toward Eldora. Middle Boulder Creek Campsites available! Diamond Lake Stats Trail: Diamond Lake Trail #975 from Fourth of July Trailhead Forest Service description and regulations [pdf] Roundtrip distance on trail: 5.2 miles Transit time from Boulder to trailhead: 55 minutes Hike time to lake: 2 hours Hike time back: 1 hour Map View Larger Map Amazon.com Widgets

It's Obvious... Not: Charged Particle Motion in a Magnetic Field and Third Order Homgeneous Differential Equations

This installment of “It’s Obvious. Not!” looks at: Book: “Classical Dynamics of Particles and Systems” Edition: third Authors: Jerry B. Marion and Stephen T. Thornton Publisher: Harcourt Brace Jovanovich Page: 68 This post looks at Example 2.10 that investigates the motion of a charged particle in a magnetic field. The example is fairly straightforward with one exception. When determining the equations of motion, the authors propose a solution for the system of differential equations discussed below and reference example C.2 of Appendix C. It’s not immediately apparent how to use Example C.2 to arrive at the authors’ solution, so the steps are outlined in detail here. If you have questions, or suggestions, all comments are always welcome! The original system of coupled differential equations is: First, the authors’ differentiate both equations and then substitute the results into the other: at this point, the book suggests using the technique of ex...

Boulder on a Random Wednesday Night!

Blood Donor Opportunity in Austin on September 6th

For those interested in donating blood, dominoes, fire trucks, or Shriners, especially in the Austin area, read on. You can donate blood and see all the rest on September 6th. A Day of Caring & Sharing - Save a Life Saturday, Sept. 6, 2008 Ben Hur Shrine Center 7811 Rockwood Dr , Austin 512-480-0812 Activities Presented by: The Ben Hur Shriners The Blood Center of Central Texas Texas Fire Marshal’s Fire Safety House Austin Fire Department Fire Truck The Ben Hur Shrine Clowns Benefitting: - Shriners’ Hospitals for Children Burn Hospital in Galveston, TX - Austin Children and Adults as they learn Fire Safety Skills Please read or post: Join the Ben Hur Shriners, The Blood Center and the Texas Fire Marshal, Saturday, September 6. 2008 at the Ben Hur Shrine Center located at 7811 Rockwood Drive, Austin for a Day of Caring and Sharing – Save a Life. From 10-2 PM The Blood Center will be in the ...

Table of Contents for App Engine Facebook Articles

Table of Contents Introduction Setup Authentication Flow Inviting Friends Appendix A: StumbleUpon Bookmarks

Rain and Rainbows at Great Sand Dunes National Monument